Lightning Electromagnetic Pulse Functions and Protecting the Artemis Spacecraft
Lightning produces some of the most powerful electric currents found on Earth, which are usually measured near the bottom or base of the lightning channel. However, these lightning “channel-base currents” also produce Electromagnetic Pulses (EMPs) which are powerful enough to be measured from the other side of the world. In this thesis, we introduce new channel-base current functions to represent lightning waveforms measured near the Artemis spacecraft, and we demonstrate that our functions can meet standard “Component A” specifications more closely than contemporary standards. We work with transcendental equations to peak-correct or “normalize” these functions, then solve for parameters graphically. To calculate the electromagnetic fields from lightning, we derive integrals from Lorenz and Maxwell’s equations, and we evaluate these integrals utilizing the lightning Transmission Line (TL) model, introduced by Uman and McLain in 1969. We assume the lightning return stroke rises at the speed of light to obtain perhaps some of the first analytical solutions to the TL model, using Euler substitution, hyperbolic substitution, integration by parts, and image theory to account for reflections. We also introduce a new polynomial substitution method as a possible alternative to Euler substitution. Finally, we introduce two new lightning models: the first resembles the Modified Transmission Line with Exponential decay (MTLE) model, while the second is likely the first model to have a variable return stroke speed. We additionally present several methods for protecting sensitive assets such as the Artemis spacecraft from lightning, both on the ground and during flight. We construct Computational Electromagnetics (CEM) models of Artemis and Launch Pad 39B using the Finite Element Method (FEM) in the time domain. We model a complex network of hanging catenary cables, each displaced by gravity and tension from other cables, and we encode them into cubic Bézier curves. We model the true shape of a lightning channel based on photographs from different vantage points, then simplify this geometry using an antenna array and a radiation pattern. We utilize Three-Dimensional Elevation Program (3DEP) data to construct the ground terrain surrounding our model. Finally, we compare our analytical and computational results to measurements.
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